COSMO chemical potential

As a result of Eq. (11) we are able to calculate the chemical potential of any molecule X in any liquid system S, relative to the chemical potential in a conductor, i.e. at the North Pole. Hence, COSMO-RS provides us with a vehicle that allows us to bring any molecule from its Uquid state island to the North Pole and from there to any other liquid state, e.g. to aqueous solution. Thus, given a liquid, or a reasonable estimate of AGjis of a soUd, COSMO-RS is able to predict the solubility of the compound in any solvent, not only in water. The accuracy of the predicted AG of transfer of molecules between different Uquid states is roughly 0.3 log units (RMSE) [19, 22] with the exception of amine systems, for which larger errors occur [16, 19]. Quantitative comparisons with other methods will be presented later in this article. 

Translating the thermodynamic concept of interacting surfaces to our basic COSMO-RS, the residual part of the chemical potential of a compound i in a solvent S is found by a summation of the chemical potentials of the surface segments of i. Starting from Eq. (5.10) we have... 

Although COSMO-RS generally provides good predictions of chemical potentials and activity coefficients of molecules in liquids, its accuracy in many cases is not sufficient for the simulation of chemical processes and plants, because even small deviations can have large effects on the behavior of a complex process. Therefore, the chemical engineer typically prefers to use empirical thermodynamic models, such as the UNIQUAC and NRTL, for the description of liquid-phase activity coefficients with... 

As we have seen before, COSMO-RS is able to describe the chemical potentials of compounds in almost any pure or mixed liquid phase, as long as the chemical composition of the liquid is known and as long as it can be considered as a chemically homogeneous phase. While this has opened an enormously broad range of applications in chemical engineering, these limitations exclude COSMO-RS from a number of important application areas in environmental simulations, life-science modeling, and product development. 

Since COSMO-RS allows for a rather fundamental calculation of the chemical potential of molecules in various chemical environments, there are many application areas that go beyond the calculation of activity and partition coefficients, which are directly accessible from the differences of chemical potentials in different phases. Often, such applications require the addition of some empiricism to the model because they involve free-energy contributions that are not directly accessible by COSMO-RS. Nevertheless, in many cases, the COSMO-RS is a robust starting point for such empirical extensions, and the resulting models are still less empirical and more fundamental than many other approaches. Without going into details we will describe some extended application areas in this chapter. 

Indeed, prediction of the change of the equilibrium constants of a chemical reaction in a variable liquid environment requires nothing other than the prediction of the chemical potentials or activity coefficients of the starting materials and products in the liquids. Thus, this task can be performed simply by using the standard COSMO-RS capabilities. Successful applications of this... 

As a final attempt to understand the origin of the unexpectedly low slope, we split AG into four different parts, i.e., the quantum chemical gas-phase dissociation, the COSMO-interaction energies of the neutral and the ionic species and the chemical potential difference from COSMO-RS. On the basis of these reasonably independent descriptors, we performed a multilinear regression of pKa yielding an almost identical regression coefficient and rms error as before with slopes ranging from 0.55 to 0.62 for the four contributions. Thus all contributions—although very different in nature—show the same unphysical slope with respect to the pKa. 

Although I did not know about the concept of the combinatorial contribution, I recognized the need for such a correction even in the initial version of COSMO-RS [C9]. Since at that time I only had in mind the calculation of infinite-dilution partition coefficients and of vapor pressures, I only cared about a solvent-size correction in pure solvents. I thought of two different solvent-size effects influencing the chemical potential of a solute X in a solvent S. The first is quite obvious—in 1 mol of a homogeneous liquid S,... 

Indeed, this solvent-size correction for the chemical potentials worked well in the initial COSMO-RS parameterizations, yielding quite small values of in the region of -0.14. Thus it appeared that the two different size contributions almost cancel out, i.e., only 14% of the obvious first contribution remains. Even large size differences of up to a factor of 10 in surface area only yielded corrections of 0.8kJ/mol in the chemical potential differences between two phases these corrections were only about half of our standard deviation at that time. Therefore, not much care was taken with respect to the combinatorial contribution during the next years of COSMO-RS development. All other contributions appeared to be of much greater importance. 

The thermodynamic consistency of this expression follows directly from the fact that the chemical potential corrections are now calculated as composition derivatives of a thermodynamic potential. Since this expression left the limits of pure solvents unchanged, and since almost only these limits are of importance for our COSMO-RS parameterization data set, we could use the existing COSMO-RS parameterization in combination with the new Gibbs-Duhem-consistent solvent size correction. 

COSMO-RS is able to calculate the chemical potential (the partial Gibbs free energy) of a compound, either pure or in a mixture from the probability distribution of a. The solubility of a compound, X, can be calculated from the differences between the chemical potentials of X in solution and pure [21, 26]. COSMOS-RS not only predicts reasonable solubility values... 

Section 3 concerns the COSMO-RS approach. This is a theory that goes beyond the usual dielectric approximation, in contrast to all other CSMs, it treats solute and solvent on the same footing and it finally allows for the calculation of chemical potentials of molecules in almost arbitrary solvents. First, in Section 3.1 the principal inapplicability of the dielectric theory to electrostatic screening on a molecular scale is expounded. Section 3.2 gives the central COSMO-RS theory, i.e., an alternative ansatz for the interpretation of electrostatic screening of solutes in solvents and its combination with statistical thermodynamics. Section 3.3 illustrates the novel COSMO-RS view of solvation for some typical solvents, while Section 3.4 shows the potential of the approach using the results of a broad para-metrization and validation study. In Section 3.5 the range of applicability is outlined. 

The overall inaccuracy for the four properties is 1.7 kJ mol with respect to the chemical potentials, corresponding to a factor of 2 for the nonlogarithmic equilibrium constants. This is comparable with the results of incremental methods for the estimation of partition coefficients. Considering the relatively small number of parameters, the short history, and the broad applicability of the COSMO-RS approach, this accuracy is very satisfactory. Although there are several possibilities for further improvements of the approach, a substantial decrease of the inaccuracy below this factor of 2 will be hard to achieve. 

As has been shown in Section 3.4, COSMO-RS provides access to the thermodynamic parameters of solvents as well as of solute molecules. It provides the knowledge of the chemical potential of any compound in any fluid. Thus COSMO-RS enables the handling of almost any partition problem of compounds between liquid and gaseous phases. In this context it is important that COSMO-RS handles multicomponent mixtures without additional complications, because it does not make any mean-field approximation. Therefore multicomponent mixtures are described almost as reliably as binary mixtures or pure liquids. 

Table 1 The electronic chemical potential /i for the gas phase and 5 different solvents (using lEFPCM and COSMO) in eV ...

In the context of our ongoing efforts in the field of conceptual DFT [27, 28], we will compute the electronic chemical potential, the chemical hardness and both the global and the local electrophilicity index for a set of uncharged radical systems in solvent. The resulting radical electrophilicity scales in solvent will be compared to the previously reported gas-phase scale. For water as a solvent, two different solvation methods (EF-PCM and COSMO) will be applied to exclude artificial effects inherent to one of the two approaches. 

In addition to these external electric or magnetic field as a perturbation parameter, solvents can be another option. Solvents having different dielectric constants would mimic different field strengths. In the recent past, several solvent models have been used to understand the reactivity of chemical species [55,56]. The well-acclaimed review article on solvent effects can be exploited in this regard [57]. Different solvent models such as conductor-like screening model (COSMO), polarizable continuum model (PCM), effective fragment potential (EFP) model with mostly water as a solvent have been used in the above studies. 

FIGURE 3.25. Potential energy profiles (from B3LYP/6-13G calculations) for the clevage of 3- and 4-nitrobenzyl chloride anion radicals (a and b, respectively) in the gas phase (top) and in a solvent (middle and bottom) (from COSMO solvation calculations with a dielectric constant of 36.6 and 78.4, respectively). Dotted and solid lines best-fitting Morse and dissociative Morse curves, respectively. Adapted from Figure 3 of reference 43, with permission from the American Chemical Society. 

To support an informed analysis of the possibilities for life in the cosmos, this chapter summarizes chemical concepts needed to evaluate the plausibility of a potential exotic life form and shows how they relate to the chemistry of the life that we know. This summary is necessarily selective. Students of chemistry and related areas develop their understanding of molecular behavior and chemical reactivity through years of study that cannot be condensed into a few pages. The committee has chosen topics for emphasis to permit a discussion of terran life to support its later discussion of exotic life. 

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